39w6d, and baby's not engaged! Will I need a c-section?

I had my 39-week appointment yesterday (I'm due tomorrow) and asked my doctor to strip my membranes, but she wasn't able to do it because I'm still rock hard and pretty much closed (which is maddening, as I've been taking evening primrose oil since 36 weeks!). All she could do was manually dilate me to a fingertip. Apparently baby's head isn't dropping deep enough into my pelvis to the point where it would prompt dilation. Doctor said my best shot is to give vaginal labor a try, but she's concerned that my pelvis is going to give me a 50/50 chance of needing a c-section. Has anyone been in a similar situation and NOT needed a c-section? Doc says they won't know if I'll need the surgery until I try to labor on my own. I'm scheduled for an induction on the 14th (41w2d), if she doesn't come on her own before then. Until then, lots of sex, walking, and bouncing on the birthing ball for me! These are gonna be the longest 9 days EVER.